Binary Neural Networks (BNNs) have demonstrated significant advantages in reducing computation and memory costs, all while maintaining acceptable accuracy on various image detection tasks. Thus, BNNs have the potential to support practical cognitive tasks on resource-constrained platforms, such as edge computing devices. To realize this, SRAM-based digital Computation-in-Memory (CIM) has gained growing attention as it overcomes the analog CIM architecture bottlenecks such as limited computing accuracy due to process variation, non-linearity, power and area-hungry Analog-to-Digital Converters (ADCs), etc. However, digital CIM architectures are highly dominated by power-hungry adder-trees, which can nullify the benefits of SRAM-based digital CIM. To address this issue, this paper proposes an adder free SRAM-based digital CIM, AFSRAM-CIM, for BNN acceleration. The proposed CIM architecture utilizes a multi-functional 10-T SRAM cell-based crossbar array and a new energy-efficient approach to perform the popcount operation. Simulation results using the MNIST dataset show that the proposed architecture maintains the state-of-the-art inference accuracy of 99.21% with only 11.86 fJ energy per operation. Moreover, AFSRAM-CIM achieves over 3× energy and ≈17× area savings when compared to the conventional digital CIM approaches.